Integrated MSc-PhD Program

SYLLABUS

KSM4E04: Riemann Surfaces

Topics covered: The definition of Riemann surfaces, elementary properties of holomorphic mappings, homotopy of curves, the fundamental group, branched and unbranched coverings, the universal covering and covering transformations, sheaves, analytic continuation, algebraic functions, differential forms, the integration of differential forms, compact Riemann surfaces, cohomology groups, Dolbeault’s Lemma, a finiteness theorem, the exact cohomology sequence, the Riemann-Roch theorem, the Serre duality theorem.

Suggested texts:

1. 1. 1. 1. 1. 1. Lectures on Riemann Surfaces by Otto Forster
               2. Riemann Surfaces by Simon Donaldson
               3. Riemann Surfaces by Way of Complex Analytic Geometry by Dror Varolin